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1. Binary to Gray
2. Binary to excess 3
3. Gray to Binary
4. BCD to binary
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Wow I didn't even know there were workbooks.

Those boxes with the $\oplus$ in them - is that XOR ? If so, is that a single input XOR there beside the MSB ?
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I was right - a line is missing there from the MSB into the first XOR. I dug out the original question for you - https://gateoverflow.in/167469/isro-2017-ece-computational-circuits. Note that and the AND and OR gates are interchanged.

My approach for these questions will be to simply choose 2 very unique binary values and check the output and compare with known codes. Should not take more than a couple of minutes.

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If so, is that a single input XOR there beside the MSB

That is why i posted. So wrong write?

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Btw how did you find out the original question?
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Googling is an art lol.

And yes, the question is wrong - but you could try and solve it for practice. Although I don't think you'll learn any new concepts here.